Academics · Adult Learning · Everyday math

Percents, worked out
where you can see them.

Type the numbers from a price tag, a bill or a pay raise. You get the answer, a bar that shows the parts, every step in order and, when the numbers allow, a way to do it in your head.

Open the percent benchWhat you get
7everyday questions worked step by step
3practice levels, eight questions a round
794practice questions, each checked twice

The percent bench

Pick the kind of question, type what you know and read the steps. Then try a practice round.

Loading the percent bench. If nothing appears, turn on JavaScript.

Four percents worth knowing by heart

Most everyday percents can be built from these four. The tool shows the build whenever the numbers come out even.

50%

Half

50% of $80.00 is $40.00. Cut it in two.

25%

Half, then half again

25% of $80.00 is $20.00. A quarter.

10%

Move the point one place

10% of $80.00 is $8.00.

1%

Move the point two places

1% of $80.00 is $0.80.

Build the rest from those. 15% is 10% plus half of 10%: $8.00 + $4.00 = $12.00. 6% is six 1%s: 6 × $0.80 = $4.80. 75% is a half plus a quarter. When the numbers are awkward, round the amount to the nearest dollar first and call the answer “about”.

What you get

Academics · Adult LearningFree

What you finish with
The answer to a real percent question with every step shown, a picture of the parts, and a mental shortcut when one exists. Over time: practice rounds at three levels, first-try results by skill and a named skill to work on next. A printed practice sheet with a worked answer key.
Who it is for
Adults brushing up on everyday math, learners preparing for a high school equivalency or placement test, English learners who know the math and want the words, and tutors or adult education teachers who want worked examples with a learner’s own numbers.
Format
Browser tool with three parts: Work it out, Practice and My progress. Works on a phone, tablet or computer, by touch or keyboard. Prints a 12-question practice sheet with a worked key; saves progress as a .csv.
Access
Free. No account and no sign-in. The numbers you type and your practice results are saved only in this browser; nothing is sent to Caveat.
Where it lives
The Adult Learning space in Caveat Academics.
Support
Questions, a correction or a request: team@caveatacademic.com.
Two discounts in a row. The second percent is taken from a price that is already lower, so the two do not simply add.

How to use it

  1. Pick the kind of question, such as Sale price and tax, and type the numbers you have.
  2. Read the answer, then the picture and the steps. If there is an In your head box, try it without a calculator.
  3. Open Practice, pick a level and answer eight questions. A miss gets a hint and a second try.
  4. Open My progress to see which skill to work on next, or print a practice sheet for later.

Open the percent bench

How the percent bench stays right

Exact arithmetic in whole cents, one rounding rule, and every practice answer checked twice.

How the answers are worked out

  • Whole cents, never fractions of a cent. Money is held as a whole number of cents and a percent as thousandths of a percent, so 8.875% of $19.99 is worked out exactly and then rounded once.
  • Rounding is to the nearest cent, half a cent going up, and the steps say so whenever an answer was rounded.
  • Tax comes after the discount. The tool taxes the sale price. Rates and special cases are set by states and cities, so a real receipt can differ by a cent or two.
  • Practice answers are marked to the cent for money and to the nearest tenth for a percent. A typed dollar sign, comma or percent sign is ignored.
  • Every practice question the page can make (794 in all) was worked out a second way with exact fractions before the page was built.

For a teacher or tutor

Start in Work it out with a real receipt, a pay stub or a sale flyer the learner brings in. Ask for a guess before the numbers go in, then compare the guess with the picture.

The three places adults most often go wrong are built in: adding the percent back to find a first price, adding two discounts together, and measuring a change against the new amount. Each has a note that names the slip.

My progress shows first-try results by skill, so the next session can start where the learner is weakest. The printed sheet has a worked key for independent study.

The seven questions and the rule behind each

QuestionRule
Sale price and taxdiscount = price × percent off; sale price = price − discount; tax = sale price × tax rate; total = sale price + tax
Tip and splittip = bill × tip percent; total = bill + tip; each share = total ÷ people, rounded up to the next cent
Percent of an amountpercent ÷ 100 × amount
What percent is itpart ÷ whole × 100, to one decimal place
Percent change(new − old) ÷ old × 100, to one decimal place, always measured against the old amount
Price before the discountsale price ÷ (1 − percent off ÷ 100)
Two discounts in a rowsecond discount taken from the price after the first; combined percent = a + b − a × b ÷ 100

Sources

  1. U.S. Department of Education, Office of Career, Technical, and Adult Education, College and Career Readiness Standards for Adult Education (2013), Mathematics Level D, Ratios and Proportional Relationships: finding a percent of a quantity as a rate per 100 and solving for the whole given a part and the percent (6.RP.3c), and multistep percent problems including tax, markups and markdowns, gratuities and percent increase and decrease (7.RP.3).
  2. Common Core State Standards for Mathematics (2010), 6.RP.A.3c and 7.RP.A.3, and 7.EE.A.2 on rewriting an expression to show how quantities are related (“increase by 5%” is the same as “multiply by 1.05”).
  3. The arithmetic is checked by an exact reference written for this page (guide/suite/pdp_ref.py): whole cents and exact fractions, with decimal rounding half up as a second method.

Example prices and rates are made up. Sales tax rates and rules are set by states and cities and are not built into this tool: type the rate printed on your own receipt. Practice with the ideas, not a full math course. Support: team@caveatacademic.com.